Preheat the oven to 325°F (162°C) and line an 8-inch square baking pan with parchment paper or foil, leaving an overhang on two opposite sides.
In a medium saucepan over medium-low heat, melt the butter completely. Remove from heat immediately once melted.
While the butter is still hot, stir in the sugar, cocoa powder, vanilla extract, and salt. Mix until fully combined. The mixture will look gritty.
Let the mixture cool for 5 to 10 minutes until it's warm but not hot to the touch.
Add the cold eggs one at a time, stirring vigorously after each addition until the batter is smooth and thick.
Add the flour and stir vigorously for about 40–50 strokes until the batter becomes very thick and begins to pull away from the sides of the pan.
Stir in chopped nuts or chocolate chips, if using.
Spread the thick batter evenly into the prepared pan, pressing it into the corners and smoothing the top.
Bake for 20 to 30 minutes, or until the edges are set and a toothpick inserted in the center comes out with moist crumbs.
Let the brownies cool completely in the pan. Then lift them out using the parchment overhang, slice into 16 squares, and serve.